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arXiv · 2502.19709

Bialgebras, Manin triples of Malcev-Poisson algebras and post-Malcev-Poisson algebras

Fattoum Harrathi·Sami Mabrouk·Nasser Nawel·Sergei Silvestrov
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Abstract

A Malcev-Poisson algebra is a Malcev algebra together with a commutative associative algebra structure related by a Leibniz rule. In this paper, we introduce the notion of Malcev-Poisson bialgebra as an analogue of a Malcev bialgebra and establish the equivalence between matched pairs, Manin triples and Malcev-Poisson bialgebras. Moreover, we introduce a new algebraic structure, called post-Malcev-Poisson algebras. Post-Malcev-Poisson algebras can be viewed as the underlying algebraic structures of weighted relative Rota-Baxter operators on Malcev-Poisson algebras.

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Fattoum Harrathi, Sami Mabrouk, Nasser Nawel, Sergei Silvestrov. 2025-02-27. Bialgebras, Manin triples of Malcev-Poisson algebras and post-Malcev-Poisson algebras. https://arxiv.org/abs/2502.19709

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